Find the derivative an determine the values

  1. Suppose [tex] f(x) = \frac{(x-3)^{4}}{x^{2}+2x} [/tex]. Find the derivative an determine the values for which it is equal to 0. So [tex] f'(x) = \frac{x^{2}+2x(4(x-3)^{3}) - (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} [/tex]. But now how would I go about finding the values for which the derivative equals 0? [tex] f'(x) = \frac{x^{2}+2x(4(x-3)^{3}) (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} = 0 [/tex]. Is it possible to factor?

  2. jcsd
  3. For any fraction, let's call it [itex]\frac{A}{B}[/itex], which part will make the whole thing equal to 0? A or B?
  4. A

    will yeah
  5. BobG

    BobG 2,351
    Science Advisor
    Homework Helper

    You missed a set of parentheses.
  6. TD

    TD 1,021
    Homework Helper

    Your derivative isn't correct yet, make sure you check that first!
  7. HallsofIvy

    HallsofIvy 41,260
    Staff Emeritus
    Science Advisor

    The derivative is correct, assuming that the missing parentheses BobG mentions is put in correctly!
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